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  <h1>Modelling to price</h1>
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<p class="toc_title">Contents</p>
<ul class="toc_list">
  <li><a href="#question_1">Two approaches</a>
    <ul>
      <li><a href="#question_1_1">Formula based approach</a></li>
      <li><a href="#question_1_2">Profit - testing approach</a></li>
    </ul>
  <li><a href="#question_2">Other factors</a>
    <ul>
      <li><a href="#question_2_1">(1)	Taxation</a></li>
      <li><a href="#question_2_2">(2)	Cost of capital</a></li>
      <li><a href="#question_2_3">(3)	Margins for adverse future experience</a></li>
      <li><a href="#question_2_4">(4)	Cost of options and guarantees</a></li>
      <li><a href="#question_2_5">(5)	Valuation basis used for statutory reserves</a></li>
      <li><a href="#question_2_6">(6)	Experience-rating to adjust premiums</a></li>
    </ul>
  <li><a href="#question_3">Testing for robustness</a>
  <li><a href="#question_4">Setting the market premium </a>
  <li><a href="#question_5">Financing pension scheme benefits</a>
    <ul>
      <li><a href="#question_5_1">(1)	Lump sum in advance</a></li>
      <li><a href="#question_5_2">(2)	Terminal funding similar to PAYG</a></li>
      <li><a href="#question_5_3">(3)	Regular contributions</a></li>
      <li><a href="#question_5_4">(4)	Smoothed PAYG</a></li>
    </ul>
  <li><a href="#question_6">Determining the level of contributions </a>
    <ul>
      <li><a href="#question_6_1">In case of shortfall</a></li>
      <li><a href="#question_6_2">In case of surplus</a></li>
    </ul>
</ul>
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Reasons for changes in practice
<ul>
  <li>
    make up loss in the past
  </li>
  <li>
    claim experience is expected to be worsened
  </li>
  <li>
    existing pricing structure is leading to losses (or insufficient profits), as premiums charged
      are insufficient to cover the cost of claims and expenses
  </li>
  <li>
    existing pricing structure is leading to lower volumes of business, as competitors charge
    cheaper premiums
  </li>
</ul>
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    <span id="question_1">Two approaches</span>
    <div id="content">
      <span id="question_1_1">Formula-based approach</span>
      EPV of future gross premiums = EPV of future benefits + EPV of future expenses + appropriate profit loadings
      <span id="question_1_2">Profit - testing approach</span>
      Alternatively, a profit-testing (or discounted cash flow) approach could be adopted based on a specified profit criterion (e.g. NPV of expected future profits equal to x% of EPV of future premiums).
      <br>
      In some cases, the contribution to profits may be negative.
      <br>
      Reasons:
      <ul>
        <li>
          Cross-subsidy of new products and renewal products
        </li>
        <li>
          loss-leading products: some insurers sell loss-leading products to attract policyholders in the expectation of cross-selling more profitable products to the same customers in the future.
        </li>
      </ul>
      However, in practice, there are many other factors to be considered by the actuary before setting the actual premium to be charged for a particular product.
    </div>
  </div>

  <div class="column middle" >
    <span id="question_2">Other factors</span>
    <div id="content">
      <span id="question_2_1">(1)	Taxation</span>
      <br>
      Tax will often be payable on profits and/or investment income and gains. In addition, tax relief may apply to expenses incurred.
      <br>
      formula-based: use investment return net of tax – but, difficult if tax is based on profit achieved (rather than on investment returns)
      <br>
      DCF: can have an explicit cash outflow for tax liability (based on investment return or overall profit, as required)
      <br>
      Thus, the company is exposed to the risk of future changes in the taxation basis
      <br>
      <span id="question_2_2">(2)	Cost of capital</span>
      <br>
      return required by providers of capital (e.g. shareholders – should reflect risks involved, lenders – should reflect interest rate paid on capital borrowed).
      <br>
      DCF: this can be reflected in the risk discount rate used.
      <br>
      formula-based: more difficult to allow for this, as there is no specific component reflecting the cost of capital. in practice, this would be allowed for in the required profit margin (e.g. higher risk → higher cost of capital → higher profit margin).
      <br>
      <span id="question_2_3">(3)	Margins for adverse future experience</span>
      <br>
      formula-based: With a formula-based approach, these will typically be allowed for by using prudent valuation assumptions. But, this is subjective and the combined effect of the margins can be difficult to determine.
      <br>
      DCF: could also project cash flows using prudent assumptions. but, better to project cash flows using “best estimate” and discount profit signature at a higher rate of interest (to allow for risks).
      <br>
      <span id="question_2_4">(4)	Cost of options and guarantees</span>
      <br>
      formula-based: It is difficult to allow accurately for the expected cost of many options and guarantees.
      <ul>
        <li>
          Convertible/renewable option: project cash flows in and out assuming that option is exercised at maturity (assumptions may reflect experience of those lives likely to exercise option). difference between outgo and income gives expected cost of option at maturity. multiply by probability of exercising option and discount to start of initial contract to give expected cost at outset.
        </li>
        <li>
          Guarantee on market rates: difficult. because, depending on future interest rates assumption, guarantee will either apply with probability 1 or will not apply.
        </li>
      </ul>
      DCF stochastic model: the additional cash flow arising from the option or guarantee under a range of ‘possible future scenarios can be assessed. Then, the expected cost (and, hence, present value) of the option or guarantee can be calculated (and included in the calculation).
      <br>
      <span id="question_2_5">(5)	Valuation basis used for statutory reserves</span>
      The basis used to calculate the statutory reserve is likely to be more prudent than the premium basis. because aim is to demonstrate ability to pay promised benefits as they fall due.

      As the return expected from investing the statutory reserve is likely to be lower than the cost of capital (or the shareholders required return), the PV of these future profits will be reduced. Thus, it may be appropriate to charge a slightly higher premium.
      <br>
      <span id="question_2_6">(6)	Experience-rating to adjust premiums</span>
      Experience-rating systems are often used in non-life insurance business such as motor and household contents insurance
      <br>
      The basic principle involved is that premiums are set separately for different classes of policyholders on the basis of their previous claims experience.
      <ul>
        <li>
          main advantages: better reflects risk of each individual policy, can also encourage policyholders to take less risk (and, thus, reduce total claims costs).
        </li>
        <li>
          main disadvantages: more complicated (and, hence, costly) to administer, may be unfair if claim was not policyholder’s fault, disputes
        </li>
      </ul>
      Protected NCD schemes allow the policyholder to make a claim without necessarily reducing the level of discount applied.
      In life insurance, there is no experience rating, as a claim is only made once
    </div>
  </div>

  <div class="column middle" >
    <span id="question_3">Testing for robustness</span>
    <div id="content">
      It is important to investigate the suitability of the premium structure under a range of different scenarios.
      <ul>
        <li>
          economic scenarios – e.g. investment returns are lower than expected
        </li>
        <li>
          demographic/statistical scenarios – e.g. mortality rates are higher (or lower) than expected, claim frequencies and/or claim amounts are higher than expected
        </li>
        <li>
          business scenarios – e.g. expenses are higher than expected, withdrawal rates are higher than expected, new business volumes are lower (or higher) than expected, mix of business is different to that expected
        </li>
      </ul>

    </div>
  </div>

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    <span id="question_5">Financing pension scheme benefits</span>
    <div id="content">
      There are a number of other reasons why the premium actually charged will differ from the “true” cost calculated.
      <ul>
        <li>
          the distribution channel used may allow the insurer to charge a premium above the market price
          <br>
          ─ e.g. tied agents and direct sales forces are subject to lower competition and less direct price comparison
          <br>
          ─ also, economies of scale may allow lower premium
        </li>
        <li>
          the number of providers in the market will affect the level of competition (and, hence, the price that can be charged)
          <br>
          ─ in practice, this can vary considerably over time, leading to an insurance cycle (i.e. companies enter/leave market when profits are high/low → increased/decreased levels of competition over time)
        </li>
      </ul>

      <span id="question_5_1">(1)	Lump sum in advance</span>
      <ul>
        <li>
          A lump sum payment equal to the EPV of the future benefit is made as soon the benefit entitlement begins to accrue.
        </li>
        <li>
          Advantages: provides maximum security of accrued benefits.
        </li>
        <li>
          Disadvantages: costs could be very volatile over time, inefficient use of funds (as money is tied up unnecessarily), what happens if full amount is not needed (e.g. on withdrawal)? excessive prudence (impractical for members to expect such a level of prudence).
        </li>
      </ul>
      <span id="question_5_2">(2)	Terminal funding similar to PAYG</span>
      <ul>
        <li>
          A lump sum payment equal to the EPV of the future benefit is made as soon as the first tranche of the benefit becomes payable.
        </li>
        <li>
          In practice, this means that a single payment may be made to an insurance company to purchase an immediate annuity on retirement (or for a spouse’s pension on death in service).
        </li>
        <li>
          Similar to PAYG for active members of the scheme, but with added security for current pensioners.
        </li>
        <li>
          because, prior to retirement, there is no fund held for members. however, on retirement, the full amount of the benefit is secured (e.g. by buying an annuity from an insurance company).
        </li>
      </ul>
      <span id="question_5_3">(3)	Regular contributions</span>
      Contributions are paid at regular intervals (e.g. monthly or annually) to build up a fund to meet the expected future benefits.
      <br>
      Depending on how the benefit is defined, the regular contribution per unit time may be defined as:
      <ul>
        <li>
          a level percentage of salary for each member
        </li>
        <li>
          a fixed amount (in monetary terms) in respect of each member
        </li>
        <li>
          a fixed amount (in real terms) in respect of each member
        </li>
      </ul>
      Advantages:
      <br>
      allows for flexible pace of funding (that can reflect current financial position of employer,
      subject to funding level of scheme). also, consistent with how benefits are accrued over working lifetime.
      <br>
      <span id="question_5_4">(4)	Smoothed PAYG</span>
      Given the impracticality of a pure PAYG system, a smoothed version is commonly used to fund State pension benefit schemes.
      <br>
      the system maintains a small fund for use purely as a working balance reflecting:
      <ul>
        <li>
          differences in timings of contribution income (from taxation) and benefit outgo
        </li>
        <li>
          uncertainty in level of benefit required (even in the short term)
        </li>
        <li>
           political difficulties inherent in changing the contribution income as required to meet benefit outgo
        </li>
      </ul>
    </div>
  </div>

  <div class="column middle" >
    <span id="question_6">Determining the level of contributions</span>
    <div id="content">
      For a defined-benefit pension scheme, the standard contribution rate (required to cover the cost of the future service benefits) will usually be adjusted to reflect any difference between the current value of the assets held and the current value of the accrued (i.e. past service) liabilities.
      <br>
      Projected Unit Method the standard contribution rate over the coming year is given by:
      <br>
      EPV of benefits accruing in the next year to current members/EPV of salaries received over the next year by current members
      <br>
      In this case, benefits accruing in the next year are based on projected final salary at retirement.
      <ul>
        <li>
          <span id="question_6_1">In case of shortfall</span>
          <br>
          <br>
          If there is a shortfall, then the standard contribution rate will be increased for a specified future period (often known as the amortisation period) to eliminate the deficit.
          <br> Then, assuming that the shortfall is intended to be eliminated over the next k years, the adjustment to (i.e. increase in) the SCR is given by:
          <br> (current value of assets - current value of accrued liabilities)/ EPV of salaries received over next years
          <br> Suppose that a final-salary pension scheme that was fully funded (i.e. assets were sufficient to cover the accrued liabilities) at the previous valuation date now shows a significant funding deficit. How might this shortfall have arisen?
          <br> poor investment returns, salary growth higher than expected (so, accrued benefits rise), higher than expected benefit pay-outs (e.g. due to inflation, lower mortality amongst pensioners, generous early retirement benefits), contributions paid have been lower than expected, change in legislation (leading to higher value of accrued benefits), change in valuation basis (e.g. using less optimistic assumptions)
          <br> Often, regulation will require that the deficit must be eliminated within a specified period (e.g. 5 years) to provide additional security for members’ accrued benefits.
          <br> Why, in practice, might it be difficult for the sponsor to increase the contribution rate in the event of such a deficit?
          deficit may arise when sponsor has financial difficulties (e.g. poor investment returns in a recession or because sponsor has requested to reduce contributions previously)
        </li>
        <li>
          <span id="question_6_2">In case of surplus</span>
          <br>
          <br>
          Similarly, if there is a surplus (i.e. current value of assets exceeds current value of accrued liabilities), then the standard contribution rate may be reduced for a specified period.
          <br>And, if the level of surplus is such that no contribution is currently required, then the sponsor may take a contribution holiday
          <br>In extreme cases, some of the surplus may be refunded to the sponsor as an immediate lump sum. However, this will usually incur a tax liability.
          <br>pension funds usually have favourable tax position (to encourage fund to “store” cash during profitable years and taking “refund” later. retirement saving). but, this could be abused to reduce tax liability by using fund to “store” cash during profitable years and taking “refund” later.
          <br>In practice, there will often be significant pressure to use some of the surplus to provide discretionary benefit increases (e.g. to pensions in payment).  members may feel that some of the surplus “belongs” to them ... particularly if the scheme is contributory. also, depends on source of surplus – e.g. if it has arisen through redundancy exercise, could be used to augment benefits on early retirement.
          <br>One of the main advantages of pre-funding pension benefits is the flexibility given to the sponsor to vary the pace of funding
          <br>In practice, why else might the scheme sponsor choose to pay a higher (or lower) contribution rate in the current year than required to cover the cost of the future benefits?
          <br>changes in current financial position of employer (e.g. pay more in good years and less in bad years), opportunity cost of contributions and alternative investment opportunities (e.g. may wish to use some of the funds to expand business), current economic conditions (may wish to avoid tying up additional funds during period of economic uncertainty).
        </li>
      </ul>
        </div>
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